This is normal kitten behaviour. Kittens don't hang about like a mature cat does, they have an overwhelming need to play. You have to continually re-direct his behaviour with toys that put you at arm's length from his claws. Anything on a stick, screwed up balls of paper or crinkly balls thrown in the air for him to catch, laser tag, you just have to wear him out with regular play. Hand these toys to your visitors as well.

Isn't there some kind of plastic tubing you can get to cover electric cords? These are particularly dangerous (and as you say, expensive to replace). You will just have to kitten-proof your living space. Put anything that might be risky out of reach or even in a drawer. Make sure he can't get at elastic bands, short pieces of string, twist ties, etc.

A kitten this young can only amuse himself for so long without getting into trouble, like a small child. If he attacks you, withdraw your attention immediately and give him a time out. As he gets older, his little brain will start to make the connection between behaviour that gets him good things (more play) and bad things (being ignored). Patience is the key.
When he climbs you, yell loudly enough to really shock him and put him back down on the floor or even in another room.
Try not to respond aggressively, it will only set things back.

Maybe the mods could make this into a new thread, biting kittens is a recurrent theme.